Landau General Physics

Mechanics and Molecular Physics
1. Auflage 2013
ISBN: 978-1-4832-8518-4
Verlag: Elsevier Science & Techn.
Format: EPUB
Kopierschutz: 6 - ePub Watermark

E-Book, Englisch, 382 Seiten

Presents, at a level suitable for undergraduates and technical college students, the basic physical theory of mechanics and the molecular structure of matter. The material contained in the work should correspond quite closely to courses of lectures given to undergraduate students of physics in Britain and America.

Autoren/Hrsg.

Landau, L D

Inhaltsverzeichnis

1;Front Cover;1
2;General Physics: Mechanics and Molecular Physics;4
3;Copyright Page;5
4;Table of Contents;6
5;Preface;10
6;CHAPTER I. PARTICLE MECHANICS;12
6.1;1. The principle of the relativity of motion;12
6.2;2. Velocity;14
6.3;3. Momentum;16
6.4;4. Motion under reactive forces;18
6.5;5. Centre of mass;19
6.6;6. Acceleration;21
6.7;7. Force;23
6.8;8. Dimensions of physical quantities;26
6.9;9. Motion in a uniform field;30
6.10;10. Work and potential energy;31
6.11;11. The law of conservation of energy;34
6.12;12. Internal energy;37
6.13;13. Boundaries of the motion;38
6.14;14. Elastic collisions;42
6.15;15. Angular momentum;47
6.16;16. Motion in a central field;51
7;CHAPTER II. FIELDS;55
7.1;17. Electrical interaction;55
7.2;18. Electric field;57
7.3;19. Electrostatic potential;60
7.4;20. Gauss' theorem;62
7.5;21. Electric fields in simple cases;64
7.6;22. Gravitational field;67
7.7;23. The principle of equivalence;71
7.8;24. Keplerian motion;73
8;CHAPTER III. MOTION OF A RIGID BODY;77
8.1;25. Types of motion of a rigid body;77
8.2;26. The energy of a rigid body in motion;79
8.3;27. Rotational angular momentum;83
8.4;28. The equation of motion of a rotating body;84
8.5;29. Resultant force;88
8.6;30. The gyroscope;89
8.7;31. Inertia forces;92
9;CHAPTER IV. OSCILLATIONS;97
9.1;32. Simple harmonic oscillations;97
9.2;33. The pendulum;101
9.3;34. Damped oscillations;104
9.4;35. Forced oscillations;107
9.5;36. Parametric resonance;113
10;CHAPTER V. THE STRUCTURE OF MATTER;116
10.1;37. Atoms;116
10.2;38. Isotopes;120
10.3;39. Molecules;122
11;CHAPTER VI. THE THEORY OF SYMMETRY;126
11.1;40. Symmetry of molecules;126
11.2;41. Stereoisomerism;129
11.3;42. Crystal lattices;131
11.4;43. Crystal systems;134
11.5;44. Space groups;140
11.6;45. Crystal classes;142
11.7;46. Lattices of the chemical elements;144
11.8;47. Lattices of compounds;148
11.9;48. Crystal planes;150
11.10;49. The natural boundary of a crystal;153
12;CHAPTER VII. HEAT;155
12.1;50. Temperature;155
12.2;51. Pressure;160
12.3;52. Aggregate states of matter;162
12.4;53. Ideal gases;164
12.5;54. An ideal gas in an external field;168
12.6;55. The Maxwellian distribution;171
12.7;56. Work and quantity of heat;177
12.8;57. The specific heat of gases;182
12.9;58. Solids and liquids;185
13;CHAPTER VIII. THERMAL PROCESSES;189
13.1;59. Adiabatic processes;189
13.2;60. Joule-Kelvin processes;193
13.3;61. Steady flow;195
13.4;62. Irreversibility of thermal processes;198
13.5;63. The Carnot cycle;201
13.6;64. The nature of irreversibility;203
13.7;65. Entropy;205
14;CHAPTER IX. PHASE TRANSITIONS;208
14.1;66. Phases of matter;208
14.2;67. The Clausius-Clapeyron equation;212
14.3;68. Evaporation;214
14.4;69. The critical point;218
14.5;70. Van der Waals' equation;221
14.6;71. The law of corresponding states;225
14.7;72. The triple point;227
14.8;73. Crystal modifications;229
14.9;74. Phase transitions of the second kind;233
14.10;75. Ordering of crystals;236
14.11;76. Liquid crystals;238
15;CHAPTER .. SOLUTIONS;241
15.1;77. Solubility;241
15.2;78. Mixtures of liquids;243
15.3;79. Solid solutions;245
15.4;80. Osmotic pressure;247
15.5;81. Raoult's law;249
15.6;82. Boiling of a mixture of liquids;252
15.7;83. Reverse condensation;255
15.8;84. Solidification of a mixture of liquids;257
15.9;85. The phase rule;261
16;CHAPTER XI. CHEMICAL REACTIONS;263
16.1;86. Heats of reaction;263
16.2;87. Chemical equilibrium;265
16.3;88. The law of mass action;267
16.4;89. Strong electrolytes;273
16.5;90. Weak electrolytes;275
16.6;91. Activation energy;277
16.7;92. Molecularity of reactions;281
16.8;93. Chain reactions;283
17;CHAPTER XII. SURFACE PHENOMENA;287
17.1;94. Surface tension;287
17.2;95. Adsorption;290
17.3;96. Angle of contact;293
17.4;97. Capillary forces;296
17.5;98. Vapour pressure over a curved surface;299
17.6;99. The nature of superheating and supercooling;300
17.7;100. Colloidal solutions;302
18;CHAPTER XIII. MECHANICAL PROPERTIES OF SOLIDS;305
18.1;101. Extension;305
18.2;102. Uniform compression;309
18.3;103. Shear;312
18.4;104. Plasticity;316
18.5;105. Defects in crystals;319
18.6;106. The nature of plasticity;323
18.7;107. Friction of solids;327
19;CHAPTER XIV. DIFFUSION AND THERMAL CONDUCTION;329
19.1;108. The diffusion coefficient;329
19.2;109. The thermal conductivity;330
19.3;110. Thermal resistance;332
19.4;111. The equalisation time;337
19.5;112. The mean free path;339
19.6;113. Diffusion and thermal conduction in gases;341
19.7;114. Mobility;345
19.8;115. Thermal diflFusion;347
19.9;116. Diffusion in solids;349
20;CHAPTER XV. VISCOSITY;352
20.1;117. The coefficient of viscosity;352
20.2;118. Viscosity of gases and Hquids;354
20.3;119. Poiseuille's formula;356
20.4;120. The similarity method;359
20.5;121. Stokes' formula;361
20.6;122. Turbulence;363
20.7;123. Rarefied gases;368
20.8;124. Superfluidity;372
21;Index;378

Leseproben

CHAPTER II

FIELDS

Publisher Summary

This chapter discusses some of the interactions underlying various physical phenomena. One of the most important kinds of interaction in nature is electrical interaction. In particular, the forces acting in atoms and molecules are essentially of electrical origin and this interaction is, therefore, what mainly determines the internal structure of various bodies. The forces of electrical interaction depend on the existence of a particular physical characteristic of particles, their electric charge. Bodies having no electric charge have no electrical interaction. As electrical interaction, gravitational interaction plays an extremely important part in nature. This interaction is a property of all bodies, whether they are electrically charged or neutral, and is determined only by the masses of the bodies. The gravitational interaction between all bodies is an attraction, the force of interaction being proportional to the product of the masses of the bodies. The chapter discusses electrical interaction and gravitational interaction. It further discusses keplerian motion.

§17. Electrical interaction

In Chapter I we have given a definition of force and the relation between force and potential energy. We shall now go on to a specific analysis of some of the interactions underlying various physical phenomena.

One of the most important kinds of interaction in Nature is . In particular, the forces acting in atoms and molecules are essentially of electrical origin, and this interaction is therefore what mainly determines the internal structure of various bodies.

The forces of electrical interaction depend on the existence of a particular physical characteristic of particles, their . Bodies having no electric charge have no electrical interaction.

If bodies may be regarded as particles, the force of electrical interaction between them is proportional to the product of the charges on the bodies and inversely proportional to the square of the distance between them. This is called . Denoting the electrical interaction force by , the charges on the bodies by 1 and 2, and the distance between them by , we can write Coulomb’s law in the form

=constant×e1e2/r2.

The force acts along the line joining the charges, and experiment shows that it is sometimes an attraction, sometimes a repulsion. Charges are therefore said to differ in sign. Bodies having charges of the same sign repel each other, while bodies having charges of opposite signs attract each other. A positive sign of the force in Coulomb’s law denotes repulsion, and a negative sign attraction. It does not matter which charges are in fact regarded as positive and which as negative, and the choice usual in physics is a historical convention. Only a difference in the sign of charges has intrinsic significance. If all negative charges were called positive and , there would be no resulting change in the laws of physics.

Since charges are now introduced for the first time and no units of charge have yet been defined, we can take the proportionality coefficient in Coulomb’s law equal to unity: = 12/2. This establishes a unit of charge, namely the charge whose force of interaction with another similar charge at a distance of one centimetre is one dyne. This is called the . The system of units based on this choice of the constant coefficient in Coulomb’s law is called the or . In this system the dimensions of charge are

e ]=([ F ][ r ]2)1/2=(g.cmsec2cm2)1/2=g1/2cm3/2sec-1.

In the SI system of units a larger unit of charge is used, called the :

 coulomb=1 C=3×109CGSE units of charge.

By means of the expression for the force of electrical interaction we can find the mutual potential energy of two electric charges 1 and 2. If the distance between these charges increases by , the work done is = 12/2. This is equal to the decrease in the potential energy . Thus

dU=e1e2dr/r2=-e1e2d(1/r),

whence

=e1e2/r.

Strictly speaking, a constant term may also be included here; we have taken it as zero, in order that the potential energy should be zero when the charges are at an infinite distance apart. The potential energy of the interaction of two charges is therefore inversely proportional to the distance between them.

§18. Electric field

Since Coulomb’s law involves the product of the charges, the force exerted on a charge by another charge 1 can be put in the form

=eE,

where E is a vector independent of the charge and determined only by the charge 1 and the distance between the charges and 1. This vector is called the due to the charge 1. Its magnitude is

=e1/r2

and it is directed along the line joining the positions of the charges 1 and . The force on due to 1 is thus the product of and the electric field at due to 1.

Thus we have another way of describing electrical interaction. Instead of saying that particle 1 attracts or repels particle 2, we say that the first particle, whose electric charge is 1, creates a particular force field in the surrounding space, namely an electric field; particle 2 does not interact directly with particle 1, but is subject to the field created by the latter.

These two ways of describing the interaction are presented here as being only formally different. In reality, however, this is not so; the concept of the electric field is by no means formal. An analysis of electric (and magnetic) fields which vary with time shows that they can exist in the absence of electric charges and are physically real in the same way as the particles that exist in Nature; however, such problems are outside the scope of the basic ideas concerning interactions of particles that are discussed here in connection with the laws of particle motion.

The electric field created by not one but several electric charges is determined by the following fundamental property of electrical interactions: the electrical interaction between two charges is independent of the presence of a third charge. From this we can conclude that, if there are several charged particles, the electric field which they create is equal to the vector sum of the electric fields produced by each particle separately. In other words, the electric fields created by different charges are simply superposed without affecting one another. This remarkable property of the electric field is called the property of .

It should not be thought that the property of superposition of electric fields is a direct consequence of the existence of electrical interaction. In reality, this fundamental property of the electric field is a law of Nature. It applies to other fields besides electric fields and plays a very important part in physics.

Let us apply the property of superposition to determine the electric field of a composite body at large distances from it. If the charges on the particles which compose the body are 1, 2, · · ·, then the fields which they create at a distance are

1=e1/r2,E2=e2/r2,…

At large distances from the body we may regard the distances from the various particles as equal and the direction, from the particles to the point considered, as constant. Thus by using the property of superposition to find the total field due to the body, we can simply take the algebraic sum of the fields 1, 2,…:

=(e1+e2+?)/r2.

We see that the field of a composite body is the same as the field of a single particle with charge

=e1+e2+?.

In other words, the charge on the composite body is equal to the sum of the charges on the particles which compose the body and does not depend on their relative position and motion. This is called the .

In general the electric field is complicated, varying from point to point in both magnitude and direction. To represent it graphically we can use ; these are lines which at every point in space have the direction of the electric field acting at that point.

If the field is created by a single charge, the lines of force are straight lines radiating from the position of the charge, or converging to its position, according as the charge is positive or negative (Fig. 18).

FIG. 18

From the definition of the lines of force it is clear that only one line of force passes through each point in space (not occupied by an electric charge), in the direction of the electric field acting at that point. Thus the lines of force do not intersect at points in space where there are no...